Finite Group Databasebeta

← Prev (#44544975) Next (#44544977) →

C3⋊((C11⋊C5)⋊D97) #44544976

order32010
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊D97)
unambiguous semidirect product(C11⋊C5)⋊D291
unambiguous semidirect productC97⋊(C3⋊AGL(1,𝔽11))
unambiguous semidirect productD3201⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C97 ⋊ C2×C5
HallC3×C11⋊C5×C97 ⋊ C2
HallD3201 ⋊ C5
HallC11⋊C5×C97 ⋊ D3
HallC11×C97 ⋊ C5×D3
HallC3×C97 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D97
SylowC97 ⋊ C3⋊AGL(1,𝔽11)
HallC11⋊C5 ⋊ D291
HallC3×C11 ⋊ C5×D97
SylowC11 ⋊ C5×D291
SylowC3 ⋊ (C11⋊C5)⋊D97

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C97C2×C5
LCSG ▷ C3×C11×C97
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 111
transitive degreeμt(G) = 3201

A minimal faithful permutation representation — 2 generators on 111 points:

(2,3)(5,9,10,8,13,6,7,14,11,12)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111);(1,2,3)(4,5,8,13,7,10,14,9,12,11,6)(15,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17)

Polycyclic presentation:

2,3,5,11,97|b^a=b^2,d^a=d^10,e^a=e^96,d^c=d^4

Conjugacy classes & character table

1026 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 26);